三维热传导型半导体器件问题在局部加密网格上的有限差分格式

Finite Difference Scheme for 3D Semiconductor Device of Heat Conduction on Grids with Local Refinement

局部网格加密技术能很好地解决局部性很强的问题,半导体器件问题的解在半导体的p-n结附近有很强的局部性质.热传导型半导体器件瞬态问题的数学模型由四个方程组成的非线性偏微分方程组的初边值问题决定,电场位势方程是椭圆型的,电子和空穴浓度方程是抛物型的,温度方程是热传导型的.依据实际数值模拟的需要,提出了一类三维热传导型半导体问题在时间上进行局部加密的复合网格上的有限差分格式,并给出了电子、空穴浓度和温度的最大模误差估计以及数值算例.这些研究结果对半导体器件数值模拟的算法理论、实际应用和工程软件系统的研制,均具有重要的价值.

The local grid refinement technique can resolve localized characteristics efficiently. The solution of the semiconductor problem device processes highly localized characteristics in the vicinity of p-n node.The momentary state of a semiconductor device of heat conduction is described by a system of four nonlinear partial differential equations.One elliptic equation is for the electrostatic,two parabolic equations are for the electron concentration and the hole concentration,and one heat exchange equation is for the temperature. According to the necessary of practical numerical simulations,a finite difference scheme for three-dimensional transient behavior of a semiconductor device of heat conduction on grids with local refinement in time is constructed and studied.Error analysis is presented and is illustrated by a numerical example.These researches are of great importance for the research on algorithmic theory,practical application and software development of numerical simulations of semiconductor devices.